I would imagine its running out of fuel or you have an air leak thats causing a soft seize. Hard to say, I would put a clear fuel filter inline and see if its still full when it bogs out and that will settle that possibility. If its still getting fuel and its bogging/dieing I would look for air leaks. How is your idle? Does it maintain or does it fluctuate a lot like high idle then low then high.
Also will it bog after 5 minutes if its just on its stand idling or do you have to be riding for it to happen? When you say bog do you mean it just sounds like poop and wont accelerate or does it stall out and die? So many things it could be.